A349622 Numbers k for which 2k-1 can be obtained with successive prime shifts towards larger primes (by iterating A003961, starting from k).

1, 2, 3, 7, 19, 25, 26, 31, 33, 37, 79, 93, 97, 139, 157, 199, 211, 229, 271, 307, 331, 337, 367, 379, 439, 499, 547, 577, 601, 607, 619, 661, 691, 727, 811, 829, 841, 877, 937, 967, 979, 997, 1009, 1034, 1069, 1171, 1237, 1279, 1297, 1399, 1429, 1459, 1531, 1609, 1627, 1657, 1759, 1867, 2011, 2029, 2089, 2131, 2137

Offset

1,2

Comments

Numbers k for which A246277(2k-1) = A246277(k). This in turn implies a looser condition A046523(2k-1) = A046523(k).

Nonsquarefree terms are rare: 25, 841 (= 29^2), 970225 ( = 5^2 * 197^2), ..., also 414690595, which is not a square. Some of these are also terms of A048674. Compare to A348511.

Links

Table of n, a(n) for n=1..63.

Index entries for sequences computed from indices in prime factorization

Prog

(PARI)
A246277(n) = if(1==n, 0, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f)/2);
isA349622(n) = (A246277(n)==A246277(n+n-1));

Crossrefs

Subsequences: A005382 (primes present), A048674 (terms requiring only one iteration to reach 2k-1).

Cf. A003961, A046523, A246277.

Cf. also A348511.

Sequence in context: A178954 A138111 A218100 * A078373 A038878 A040112

Adjacent sequences: A349619 A349620 A349621 * A349623 A349624 A349625

Keyword

nonn

Author

Antti Karttunen, Nov 26 2021

Status

approved